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BIOMD0000000267 - Lebeda2008 - BoNT paralysis (3 step model)


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Reference Publication
Publication ID: 18551355
Lebeda FJ, Adler M, Erickson K, Chushak Y.
Onset dynamics of type A botulinum neurotoxin-induced paralysis.
J Pharmacokinet Pharmacodyn 2008 Jun; 35(3): 251-267
Integrated Toxicology Division, US Army Medical Research Institute of Infectious Diseases, Fort Detrick, MD 21702-5011, USA.  [more]
Original Model: BIOMD0000000267.origin
Submitter: Vijayalakshmi Chelliah
Submission ID: MODEL1009070000
Submission Date: 07 Sep 2010 15:13:32 UTC
Last Modification Date: 18 May 2017 12:13:55 UTC
Creation Date: 07 Sep 2010 15:22:36 UTC
Encoders:  Lukas Endler
   Vijayalakshmi Chelliah
   Frank Lebeda
set #1
bqbiol:hasProperty Human Disease Ontology botulism
bqbiol:isVersionOf Reactome REACT_11184.1
Gene Ontology negative regulation of synaptic transmission, cholinergic
Gene Ontology obsolete bontoxilysin activity
Gene Ontology receptor-mediated endocytosis
Gene Ontology pathogenesis
bqbiol:hasTaxon Taxonomy Mus musculus
Taxonomy Rattus norvegicus
Taxonomy Homo sapiens
set #2
bqmodel:isDerivedFrom PubMed 6243359
Lebeda2008 - BoNT paralysis (3 step model)
The onset of paralysis of skeletal muscles induced by BoNT/A at the isolated rat neuromuscular junction is describing in the model. This is the 3-step model described in the paper. This model is the reduced form of the model developed my Simpson 1980; PMID:   6243359  , i.e., it omits three unknown parameters that represents the binding sites for each species of the toxin. The extension to this model, i.e. the 4-step model described in the paper is BIOMD0000000178.

This model is described in the article:

Lebeda FJ, Adler M, Erickson K, Chushak Y.
J Pharmacokinet Pharmacodyn 2008 Jun; 35(3): 251-267


Experimental studies have demonstrated that botulinum neurotoxin serotype A (BoNT/A) causes flaccid paralysis by a multi-step mechanism. Following its binding to specific receptors at peripheral cholinergic nerve endings, BoNT/A is internalized by receptor-mediated endocytosis. Subsequently its zinc-dependent catalytic domain translocates into the neuroplasm where it cleaves a vesicle-docking protein, SNAP-25, to block neurally evoked cholinergic neurotransmission. We tested the hypothesis that mathematical models having a minimal number of reactions and reactants can simulate published data concerning the onset of paralysis of skeletal muscles induced by BoNT/A at the isolated rat neuromuscular junction (NMJ) and in other systems. Experimental data from several laboratories were simulated with two different models that were represented by sets of coupled, first-order differential equations. In this study, the 3-step sequential model developed by Simpson (J Pharmacol Exp Ther 212:16-21,1980) was used to estimate upper limits of the times during which anti-toxins and other impermeable inhibitors of BoNT/A can exert an effect. The experimentally determined binding reaction rate was verified to be consistent with published estimates for the rate constants for BoNT/A binding to and dissociating from its receptors. Because this 3-step model was not designed to reproduce temporal changes in paralysis with different toxin concentrations, a new BoNT/A species and rate (k(S)) were added at the beginning of the reaction sequence to create a 4-step scheme. This unbound initial species is transformed at a rate determined by k(S) to a free species that is capable of binding. By systematically adjusting the values of k(S), the 4-step model simulated the rapid decline in NMJ function (k(S) >or= 0.01), the less rapid onset of paralysis in mice following i.m. injections (k (S) = 0.001), and the slow onset of the therapeutic effects of BoNT/A (k(S) < 0.001) in man. This minimal modeling approach was not only verified by simulating experimental results, it helped to quantitatively define the time available for an inhibitor to have some effect (t(inhib)) and the relation between this time and the rate of paralysis onset. The 4-step model predicted that as the rate of paralysis becomes slower, the estimated upper limits of (t(inhib)) for impermeable inhibitors become longer. More generally, this modeling approach may be useful in studying the kinetics of other toxins or viruses that invade host cells by similar mechanisms, e.g., receptor-mediated endocytosis.

To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information.

Publication ID: 18551355 Submission Date: 07 Sep 2010 15:13:32 UTC Last Modification Date: 18 May 2017 12:13:55 UTC Creation Date: 07 Sep 2010 15:22:36 UTC
Mathematical expressions
endocytosis translocation binding  
Assignment Rule (variable: tension)      
Physical entities
Compartments Species
extracellular free_BoNT/A bound_BoNT/A  
endosome transloc_BoNT/A    
neuroplasm lytic_BoNT/A    
Global parameters
Reactions (3)
 endocytosis [bound_BoNT/A] → [transloc_BoNT/A];  
 translocation [transloc_BoNT/A] → [lytic_BoNT/A];  
 binding [free_BoNT/A] → [bound_BoNT/A];  
Rules (1)
 Assignment Rule (name: tension) tension = 1-lytic
 extracellular Spatial dimensions: 3.0  Compartment size: 1.0
Compartment: extracellular
Initial concentration: 1.0
Compartment: extracellular
Initial concentration: 0.0
 endosome Spatial dimensions: 3.0  Compartment size: 1.0
Compartment: endosome
Initial concentration: 0.0
 neuroplasm Spatial dimensions: 3.0  Compartment size: 1.0
Compartment: neuroplasm
Initial concentration: 0.0
Global Parameters (1)
Value: NaN
endocytosis (1)
Value: 0.141   (Units: perminute)
translocation (1)
Value: 0.013   (Units: perminute)
binding (1)
Value: 0.058   (Units: perminute)
Representative curation result(s)
Representative curation result(s) of BIOMD0000000267

Curator's comment: (updated: 07 Sep 2010 15:22:06 GMT)

Figure 1 of the reference publication has been reproduced. The model was integrated and simulated using Copasi v4.5 31